Square Roots and Divisions

Algebra Level 2

a b − b a b a − a b \Large \dfrac{\sqrt{ \frac ab} - \sqrt{\frac ba} }{\sqrt{ \frac ba} - \sqrt{\frac ab}}

If a a and b b are distinct non-zero numbers, simplify the expression above.

a \sqrt a − 1 -1 1 1 b \sqrt b a b \sqrt{\frac ab}

Jean-Luc LeBlanc by Jean-Luc LeBlanc , 28, Canada

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Nihar Mahajan
Sep 24, 2015

The trick here is by letting x = a b , y = b a \large x=\sqrt{\dfrac{a}{b}} , y=\sqrt{\dfrac{b}{a}} . Thus the given expression becomes:

x − y y − x = − ( y − x ) y − x = − 1 \Large\dfrac{x-y}{y-x} = \dfrac{-(y-x)}{y-x} = \boxed{-1}

7 Helpful 0 Interesting 0 Brilliant 0 Confused

Yessir it's actually a lot more simple than it seems :)

Jean-Luc LeBlanc - 5 years, 8 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...